Results for non-adversarial error models. All the results mentioned above are for the adversarial error model of
Hamming [1]}, [2]}. In the setting of random corruptions (Shannon
model), the situation seems to be better understood thanks to the
seminal result on explicit polar codes of
Arikan [3]}.
More recently, in another breakthrough
Guruswami et al.  [4]} showed that polar codes can
achieve almost linear time decoding with near optimal convergence to
capacity for the binary symmetric channel. This result gives an explicit code construction
achieving parameter trade-offs similar to Shannon's randomized
construction [5]} while also admitting very efficient encoding
and decoding.
Explicit capacity-achieving constructions are also known for bounded memory
channels [6]} which restrict the power of the adversary
and thus interpolate between the Shannon and Hamming models.
